Hausdorff dimension of unique beta expansions

Derong Kong, Wenxia Li

Given an integer $N\ge 2$ and a real number $\beta >1$, let ${\Gamma }_{\beta ,N}$ be the set of all $x={\sum }_{i=1}^{\infty }{d}_i/{\beta }^i$ with $d_i\in \{0,1,\cdots ,N-1\}$ for all $i\ge 1$. The infinite…